Alternating sign matrix theorem

introduction

• PDF
• descending plane partitions and alternating sign matrix  [1]http://math.berkeley.edu/~reshetik/RTG-semin-fall-2010/Philippe.pdf[2]
• Refined enumeration of Alternating Sign Matrices and Descending Plane Partitions

 

 

 

 

 

 

 

 

 

 

 

DPP to lattice paths

P. Lalonde, Lattice paths and the antiautomorphism of the poset of descending plane partitions, Discrete Math. 271 (2003) 311–319

Descending plane partitions and rhombus tilings of a hexagon with a triangular hole C. Krattenthaler, 2006

• Rhombus tilings/Dimers or Lattice Paths for DPPs
• lattice paths (lattice fermions)
• related to non-intersecting paths
• Gessel-Viennot theorem http://qchu.wordpress.com/2009/11/17/the-lindstrom-gessel-viennot-lemma/

 

 

 

from ASM to 6 vertex model

• Kuperberg
• Izergin - Korepin

 

 

1+1 dimensional Lorentzian quantum gravity

exists quantities \phi such that if \phi(g,a)=\phi'(g',a') then [T(a,g),T(a',g')]=0

\phi(g,a)=\frac{1-g^2(1-a^2)}{ag}=q+q^{-1}

 

 

 

history

• 1983 Mills, Robbins and Rumsey ASM conjecture
• 1996 Kuperberg alternative proof of ASM conjecture using the connection with the six vertex model
• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

 

encyclopedia

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Plane_partition
• http://en.wikipedia.org/wiki/alternating_sign_matrix
• http://en.wikipedia.org/wiki/Six-vertex_model

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• Princeton companion to mathematics(Companion_to_Mathematics.pdf)

 

 

 

 

books

• 찾아볼 수학책

• Exactly Solved Models in Statistical mechanics
  
  • R. J. Baxter
• Proofs and Confirmations
  
  • Bressoud, David M.,
  • MAA Spectrum, Mathematical Associations of America, Washington, D.C., 1999.

• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

 

 

 

 

expositions

http://www.macalester.edu/~bressoud/talks/

http://www.macalester.edu/~bressoud/talks/2009/asm-Moravian.pdf

 

 

 

articles

• http://www.math.lsa.umich.edu/~lserrano/asm.pdf
• Propp, James. 2002. The many faces of alternating-sign matrices. math/0208125 (August 15). http://arxiv.org/abs/math/0208125. 
   
  
• How the alternating sign matrix conjecture was solved,
  
  • Bressoud, David M. and Propp, James,
  • Notices of the American Mathematical Society, 46 (1999), 637-646.
• Another proof of the alternating sign matrix conjecture
  
  • G Kuperberg, International Mathematics Research Notes (1996), 139-150.
• Proof of the alternating sign matrix conjecture
  
  • Zeilberger, Doron
  • Electronic Journal of Combinatorics 3 (1996), R13.
• Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase
  
  • Bleher, Pavel M.; Fokin, Vladimir V.

• 논문정리
• http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
• http://www.ams.org/mathscinet
• http://www.zentralblatt-math.org/zmath/en/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html
• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
• http://dx.doi.org/

 

 

experts on the field

• http://arxiv.org/